Supraposinormality and hyponormality for the generalized Cesàro matrices of order two

Abstract

It is well known that the generalized Cesàro matrices of order one are hyponormal operators on ℓ 2 , and it has recently been shown that the Cesàro matrix of order two is also hyponormal. Here the relatively new concept of supraposinormality is used to show that the generalized Cesàro matrices of order two are both posinormal and coposinormal, and that "most" of them are also hyponormal. A conjecture is propounded that would extend the hyponormality result.

A conjecture on hyponormality for the Cesàro matrix of positive integer order

“…where 2) is also hyponormal on ℓ 2 . (See also [7].) The computations in [6] centered on coposinormality, and the diagonal form of P emerged somewhat serendipitously from those computations.…”